Motor vehicles are often equipped with a remote keyless entry (“RKE”) system that allows a person to lock or unlock a door of the vehicle remotely. RKE systems include a portable, battery-powered radio transmitter, known as a fob, that is small enough to be carried conveniently in a person's pocket or purse. The fob includes a number of small buttons that can be pressed to activate some vehicle function via the radio link with the vehicle. In some proposed designs, a radio link is automatically established upon arrival of an authorized person at the vehicle, without overt action by the person, and the system then responds by unlocking one or more of the vehicle doors. Different technical approaches for implementing such a “passive” RKE function are shown in, for example, U.S. Pat. Nos. 4,942,393 and 6,181,254. Although, in such systems, the doors are unlocked in a hands-free manner, it is still necessary for the person to manually open, or overtly trigger the opening, of the vehicle door.